FUNCTIONAL EQUATIONS IN THE THEORY OF DYNAMIC PROGRAMMING--7: COMPLEX OPERATORS AND MIN-MAX VARIATION

Abstract

Previous papers have applied the functional equation approach of dynamic programming to the study of variational problems associated with the Sturm-Liouville equation of second order with real coefficients. In this way, it was possible to obtain the dependence of the Green's function upon the interval length. From this was obtained the corresponding dependence of the characteristic values and the characteristic functions, and similar results for vector-matrix systems. To apply the same general techniques to the study of equations with complex coefficients, min-max variation was used. It is shown that this method can be applied rigorously.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1960
Accession Number
AD0654634

Entities

People

  • R. Sherman Lehman
  • Richard E. Bellman

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Computer Programming
  • Differential Equations
  • Dynamic Programming
  • Equations
  • Euler Equations
  • Formulas (Mathematics)
  • Intervals
  • Mathematics
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis